Adjusting spatial operations based on map density

ABSTRACT

A method of determining density of a map is described along with an apparatus and computer-readable medium comprising instructions therefore. The method comprises determining one or more nodes of a quad tree applied to a map with which a predetermined query region intersects, calculating a cumulative data size of the query region based on a data size of the one or more intersecting nodes, and determining an average density of the query region based on the query region area and the cumulative data size.

BACKGROUND

Mobile mapping applications, e.g., mapping applications for execution on mobile devices such as global positioning system (GPS)-based devices, are often executed on computer-based platforms having a slower central processing unit (CPU) and limited memory in comparison to desktop computer-based platforms. Upfront knowledge of mobile mapping application resource requirements, e.g., CPU speed, memory space, etc., enables better use of the limited resources available on the computer-based platforms, improves performance of the application and provides an improved user experience during interaction with the application.

In mobile mapping applications, many spatial operations, e.g., map display, nearest search and street routing, depend on map density. Map density refers to the amount of information and/or features displayed on a given area of a displayed map. For example, it is not desirable to have too crowded map views which reduce screen readability and increase the time to update the view. At the same time, it is not desirable to have map views with very few features and which do not provide enough navigation information. The problem can be critical for mobile devices having small screens.

The map display detail level, i.e., the amount of features displayed, at a given scale is defined either in the application software or the map database. Users may be provided with a mechanism to manually adjust the map display detail level. In such situations, the setting is constant everywhere in a given map. In reality, the density of a given feature type is not evenly distributed around the world, e.g., there are many more roads per square mile in urban areas than in rural areas. The non-uniformity of feature density increases map developers difficulty in designing map views which work well both in urban areas and rural areas.

Prior approaches predefine at the time of map creation which class of features is displayed at different scales. Because the class of features is predefined for the entire map, by its nature it has to be an average and may be too dense or too sparse for some regions of the map. To adjust these possible mismatches of density, the user is provided with a user interface (UI) that allows the user to change which class of features is displayed at a particular level. Therefore, when the user is dissatisfied with the feature density displayed on the map at a particular location at a particular zoom level, the user can manipulate the UI and change the display level explicitly to be more or less dense.

The prior approach is extremely cumbersome for users especially if a mapping device is used while driving, biking, or any other similar activity when the user's hands and attention may be occupied.

Street routing algorithms also suffer from a non-uniformity of feature density. Street routing may be based on a type of greedy algorithm in which roads are divided into several function classes depending on the importance of the roads, e.g., surface roads, highways, etc. Roads in a given function class and all higher level function classes comprise a connected road network. In order to quickly find a street route between two far away points, a route search engine needs to only examine important roads, e.g., freeways, as soon as possible. In order to maintain route quality, such jumps from local streets to major roads such as highways and freeways have to meet some criteria. Prior approaches predefine the criteria constant everywhere in a given map thereby making the routing algorithm impossible to generate street routes with optimal quality and search time in both urban and rural areas.

In another case, personal navigation devices usually have a nearest (proximity) search function, which allow users to find specific types of objects near a reference point (e.g., the current position). Feature density varies by location and feature type. If a predefined search radius is used, the nearest search function may yield no result, too many results, or take too much time. Even if the search radius is adjusted based on search results, each search iteration can take significant time.

SUMMARY OF THE INVENTION

It is, therefore, an object of the present invention to resolve one or more of the foregoing difficulties by providing a method that automatically keeps the similar density of the displayed map features by deciding in real time which features should be displayed at a given location and zoom level.

This auto adjustment may be achieved by efficiently estimating in real time map density for different possible combination of map features and displaying the best found feature combination.

These and other objects of the present invention are achieved by a method of determining density of a map comprising: determining one or more nodes of a quad tree applied to a map with which a predetermined query region intersects, calculating a cumulative data size of the query region based on a data size of the one or more intersecting nodes; and determining a density of the query region based on the query region area and the cumulative data size.

The foregoing and other objects of the invention are achieved by a mobile computer device for determining density of a map, the device comprising: a processor; a memory communicatively coupled with the processor and comprising a set of instructions which, when executed by the processor, cause the processor to: determine one or more nodes of a quad tree applied to a map with which a predetermined query region intersects, calculate a cumulative data size of the query region based on a data size of the one or more intersecting nodes, and determine a density of the query region based on the query region area and the cumulative data size.

The foregoing and other objects of the invention are achieved by a computer-readable medium storing instructions which, when executed by a processor, cause the processor to determine one or more nodes of a quad tree applied to a map with which a predetermined query region intersects, calculate a cumulative data size of the query region based on a data size of the one or more intersecting nodes, and determine a density of the query region based on the query region area and the cumulative data size.

Still other objects and advantages of the present invention will become readily apparent to those skilled in the art from the following detailed description, wherein the preferred embodiments of the invention are shown and described, simply by way of illustration of the best mode contemplated of carrying out the invention. As will be realized, the invention is capable of other and different embodiments and its several details are capable of modifications in various obvious respects, all without departing from the invention. Accordingly, the drawings and description thereof are to be regarded as illustrative in nature, and not as restrictive.

DESCRIPTION OF THE DRAWINGS

The present invention is illustrated by way of example, and not by limitation, in the figures of the accompanying drawings, wherein elements having the same reference numeral designations represent like elements throughout and wherein:

FIG. 1 is a display useable in conjunction with an embodiment according to the present invention;

FIG. 2 is a display of a portion of the FIG. 1 display according to an embodiment;

FIG. 3 is a display of another portion of the FIG. 1 display according to an embodiment;

FIG. 4 is a display of the FIG. 2 display showing road text labels according to an embodiment;

FIG. 5 is a display of the FIG. 3 display showing road text labels according to an embodiment;

FIG. 6 is a display of the FIG. 2 display showing objects according to an embodiment;

FIG. 7 is a display of the FIG. 3 display showing objects according to an embodiment;

FIG. 8 is a high-level flow diagram of a portion of a sequence of instructions according to an embodiment;

FIG. 9 is a high-level flow diagram of another portion of a sequence of instructions according to an embodiment;

FIG. 10 is a high-level flow diagram of another portion of a sequence of instructions according to an embodiment;

FIG. 11 is a high-level flow diagram of another portion of a sequence of instructions according to an embodiment;

FIG. 12 is a high-level block diagram of a computer system usable in conjunction with an embodiment;

FIGS. 13 a-c are diagrams of exemplary quad trees according to an embodiment;

FIG. 14 is a diagram of a query rectangle overlaid on a quad tree according to an embodiment; and

FIG. 15 is a diagram of a query rectangle overlaid on a map spatially indexed by a quad tree.

DETAILED DESCRIPTION

A method and an apparatus for estimating map density are described along with automatically retaining a similar density of displayed map features by adjusting in real time visible features at a given location and zoom level. Methods automatically adjusting street routing and nearest (proximity) search are also described. In at least some embodiments, the adjustment of map display density, street routing and nearest search may be performed in an optimal and/or efficient manner. In the following description, for purposes of explanation, numerous specific details are set forth in order to provide a thorough understanding of the present invention. It will be apparent, however, that the present invention may be practiced without these specific details. In other instances, well-known structures and devices are shown in block diagram form in order to avoid unnecessarily obscuring the present invention.

FIG. 1 depicts a display 100 of a portion of a map 102 depicting a geographic region comprising two states 104, 105. A rural region 106 portion of map 102 is depicted in FIG. 2 as displayed at an enlarged level of detail. An urban region 108 portion of map 102 is depicted in FIG. 3 as displayed at an enlarged level of detail. Each of FIGS. 2 and 3 depicts a corresponding rural region 106 and urban region 108 comprising a set of roads in the region. As depicted, the map density of rural region 106 is less dense than the map density of urban region 108.

FIGS. 4 and 5 depict, respectively, displayed maps of urban region 106 and rural region 108 comprising text labels applied to the displayed roads.

FIGS. 6 and 7 depict, respectively, displayed maps of urban region 106 and rural region 108 comprising geographic and/or community features applied to the displayed roads. The two sample maps demonstrate the following map layers: Freeways, Freeway labels, Local streets, Local street labels, Lakes, Lake labels, Community feature and Community feature labels. To adjust map display density, layer visibility can be enabled or disabled layer by layer. In at least some embodiments, layers are enabled or disabled according to predefined relationships, e.g., a freeway label layer is disabled if freeway layer is disabled, etc.

One or more embodiments according to the present invention provide a method for automatically retaining a similar density of displayed map features by determining in real time which features should be displayed at a given location and zoom level. The automatic adjustment is performed, at least in part, by efficiently estimating map density for different possible combinations of map features and displaying a feature combination at or above a predetermined level. For example, different features as depicted in FIGS. 2-7 described above may be selectively applied to a displayed map to obtain a predetermined map density level.

1. Estimation of Map Density

One or more embodiments according to the present invention are based on the fact that many mapping systems use quad trees as a spatial index to speed up spatial queries. A quad tree is a tree-type data structure wherein each node of the tree comprises up to four child nodes in order to enable recursive partitioning of a two dimensional space, e.g., subdividing a space into four quadrants. In at least some embodiments, the nodes of a quad tree may be a different shape, e.g., squares, diamonds, parallelepipeds, etc.

FIG. 13 a depicts a first level of a quad tree, i.e., a root node 1300 of the tree covering an entire mapping layer. FIG. 13 b depicts a second level of a quad tree, i.e., root node 1300 having four child nodes 1301-1304. FIG. 13 c depicts a third level of the quad tree, i.e., each child node 1301-1304 of root node 1300 having four child nodes 1305-1308, 1309-1312, 1313-1316, and 1317-1320, respectively.

FIG. 14 depicts an area of interest, i.e., a query region (rectangle) 1400 (thick line), overlaid on quad tree 1402. For illustration purpose, nodes in the 3rd level of the quad tree are not completely expanded in this example. As depicted, query rectangle 1400 intersects with the root node of quad tree 1402, as well as, the four (4) child nodes of the second level of the quad tree and one child node of the third level of the quad tree. FIG. 15 depicts an exemplary map 1500 having a quad tree 1502 overlaid over the map. Darker portions of map 1500 correspond to increased density of roadways. A query rectangle 1504 is also overlaid on map 1500.

With the spatial index, all spatial objects are organized into a list of quads or cells with different spatial size and locations. Each quad comprises a group of objects. The quad also retains the size of the object data and/or the number of objects.

A spatial query, e.g., finding all objects intersecting with a rectangle, starts with first finding all quads intersecting with the rectangle. In at least some embodiments, user input, e.g., via a display and/or voice or other input mechanism, is received to determine a query rectangle. In at least some embodiments, the query rectangle may be determined based on a given map display and/or traversal of a path. Without checking individual objects, this operation is relatively fast. Prior to performing any spatial operations, all quads intersecting with a query rectangle may be determined and the data size within the query rectangle may be estimated with the process set forth in pseudo-code form in Listing 1.

Listing 1 EstimateDataSize (QueryRectangle) {   Find all quads intersecting with QueryRectangle   Size = 0   For each quad intersecting with QueryRectangle   {     if (quad is inside QueryRectangle) then       Size += size of quad     else     {       Size += <size of quad>*<intersecting area>/<quad area>     }   }   return Size; }

To obtain best performance, integers are used to calculate the data size of quads partially overlapping with the QueryRectangle. Mapping systems with a spatial index already have the function to find all quads intersecting with query rectangles.

After the size within a query rectangle is estimated, the size is used as the indicator of average map density inside the query rectangle. The size is relevant to the database coding schema, and the resolution of the map data. For a particular database format, experiments may be performed to set thresholds used to adjust spatial operations based on the size information. For the same database format, parameters may be set in different databases to fine tune the thresholds further.

FIG. 8 depicts a high-level process flow diagram of execution of a portion 800 of a sequence of instructions, similar to Listing 1, by a mobile device. The flow of control begins at find quad function 801. If no quads intersecting the QueryRectangle are found, the flow proceeds to return size function 802. If one or more quads intersecting the QueryRectangle are found, the flow proceeds to determine if the quad is inside the QueryRectangle at function 804.

If the outcome of function 804 is positive (YES), the flow proceeds to increment function 806 and the size is incremented by the size of the quad, e.g., an area value. If the outcome of function 804 is negative (NO), the flow proceeds to increment function 808 and the size is incremented by the size of the quad multiplied by the intersecting area divided by the quad area, e.g., the size is incremented by an amount proportional to the amount of overlap of the intersecting area.

After either of increment function 806, 808, the flow proceeds to complete determination function 810. Complete determination function 810 determines whether all quads intersecting the QueryRectangle have been included in the size determination. If the outcome of complete determination function 810 is positive (YES), the flow proceeds to return size function 802. If the outcome of complete determination function 810 is negative (NO), the flow proceeds to function 804 and evaluation of the next quad is performed as described above.

In at least some embodiments, after completion of the process flow portion 800, the determined size may be output to a memory, e.g., memory 1206, a register of processor 1204, etc., and/or an output device, e.g., a display 1208, a printer, another computer, etc.

2. Automatically Adjust Detail Level on Map Display

The above-described function estimates the map data size within a screen rectangle. With the present function, the pseudo-code of Listing 2 describes a process of adjusting detail level on the map screen.

Listing 2 nIteration =0 while (1) {   density = EstimateDataSize (ScreenRectangle)   if (density  > nMaxDensity  AND  nIteration  <     nMaxIteration  AND  Other Constraints)   {     Adjust predefined map detail levels or adjust map layer visibility   }   else if (density  < nMinDensity  AND  nIteration  <     nMaxIteration  AND  Other Constraints)   {     Adjust predefined map detail levels or adjust map layer visibility   }   else     break;   Increase nInteration by 1 } Draw map on the screen

FIG. 9 depicts a high-level process flow diagram of execution of a portion 900 of a sequence of instructions, similar to Listing 2, by a mobile device. The flow of control begins at estimate data size function 800 as described above with respect to FIG. 8, which estimates map density based on the selected map detail level and/or one or more visible map layers. The flow proceeds to maximum density comparison function 902 wherein the current map density is compared with a predetermined maximum map density. In one or more embodiments, additional comparisons may be made in comparison function 902, e.g., as indicated in Listing 2 a comparison of the number of iterations performed in portion 900 with respect to a maximum number of iterations to be performed for a given map.

If the current map density exceeds the predetermined maximum map density (positive outcome or YES), the flow proceeds to adjustment function 904. In adjustment function 904, the detail level and/or map layer visibilities may be adjusted to reduce the map density. In some embodiments, the detail levels or visibility of layers to be adjusted, may be predetermined at map creation. The flow then proceeds to return to estimate data size function 800.

If the current map density does not exceed the predetermined maximum map density (negative outcome or NO), the flow proceeds to minimum comparison determination function 906 wherein the current map density is compared with a predetermined minimum map density. In one or more embodiments, additional comparisons may be made in comparison function 906, e.g., as indicated in Listing 2 a comparison of the number of iterations performed in portion 900 with respect to a maximum number of iterations to be performed for a given map.

If the current map density falls below the predetermined minimum map density (positive outcome or YES), the flow proceeds to adjustment function 904. In adjustment function 904, the detail level and/or map layer visibilities may be adjusted to increase the map density. In some embodiments, the detail levels or visibility of layers to be adjusted, may be predetermined at map creation. The flow then proceeds to return to estimate data size function 800 with the newly adjusted map detail level and/or layer visibility.

If the current map density exceeds the predetermined minimum map density (negative outcome or NO), the flow proceeds to draw map function 908 wherein the map is drawn on a display screen.

3. Automatically Adjust Street Routing Algorithm

The functionality described in Listing 1 estimates the density of one or more selected map layers at a specific location. Adjusting the street routing criteria based on urban or rural areas based on map density, the routing performance and route quality may be significantly improved.

The pseudo-code of Listing 3 describes a process of automatically adjusting a street routing algorithm.

Listing 3 density = EstimateDataSize (QueryRectangle, selected layers) if (density > MinUrbanDensity AND Other Constraints) {   Search routes with the criteria for urban areas } else {   Search routes with the criteria for rural areas }

FIG. 10 depicts a high-level process flow diagram of execution of a portion 1000 of a sequence of instructions, similar to Listing 3, by a mobile device. The flow of control begins at estimate data size function 800 as described above with respect to FIG. 8. To estimate data density of one or more selected layers, a QueryRectangle having a predefined size and centered at the location of interest is used. The flow proceeds to function 1002 wherein the current map density is compared with a predetermined minimum urban density. In one or more embodiments, additional comparisons may be made in determine function 1002.

If the current map density exceeds the predetermined minimum urban density (positive outcome or YES), the flow proceeds to urban route search function 1004. In urban route search function 1004, a route based on a user-determined and/or mobile device-determined source and destination is determined based on criteria for urban areas. Examples of such criteria comprise the minimal search distance before jumping to highways or freeways and estimated (heuristic) distance from current position to destination.

If the current map density does not exceed the predetermined minimum urban density (negative outcome or NO), the flow proceeds to rural route search function 1006 with criteria for rural areas. In rural route search function 1006, a route based on a user-determined and/or mobile device-determined source and destination is determined based on criteria for rural areas. Examples of such criteria comprise the minimal search distance before jumping to highways or freeways and estimated (heuristic) distance from current position to destination.

After a route is determined based on either of search rural route function 1006 and search urban route function 1004, the flow proceeds to return function 1008 and execution proceeds to perform other tasks.

4. Auto Adjustment of Nearest Search

With the data size estimate function 800 described in Listing 1, the search radius of nearest search may be adjusted automatically before the actual search is performed. This improves search performance and search result quality.

The pseudo-code of Listing 4 describes a process of automatically adjusting a nearest search algorithm.

Listing 4 nIteration =0 datasize = 0 Radius = initial Radius while (datasize< MinDataSize AND nIteration < nMaxIteration) {   Enlarge Radius by 2   QueryRectangle = bounding box of the circle centered at the     reference point with Radius   datasize = EstimateDataSize (QueryRectangle, selected layers)   Increase nIteration by 1 } NearestSearch (Radius, reference point)

FIG. 11 depicts a high-level process flow diagram of execution of a portion 1100 of a sequence of instructions, similar to Listing 4, by a mobile device. The flow of control begins at data size comparison function 1102 wherein the current map data size is compared to a predetermined minimum data size value. In one or more embodiments, the search Radius is set to a small initial value, and the initial map data size is set to a default value of zero at the beginning of the control flow. In one or more embodiments, data size comparison function 1102 comprises additional comparisons, e.g., a comparison of the number of iterations in which portion 1100 has been performed with respect to a predetermined maximum number of iterations. As depicted in Listing 4 above, portion 1100 completes if the predetermined maximum number of iterations has been exceeded.

If the current map data size does not exceed the predetermined minimum data size (negative outcome or NO), the flow proceeds to enlarge radius function 1104 wherein the search circle is increased in diameter, e.g., multiplied by 2. The QueryRectangle bounding the search circle is enlarged accordingly. The flow proceeds to estimate data size function 800 as described above with respect to FIG. 8 using the newly enlarged QueryRectangle. The flow then proceeds to return to data size comparison function 1102.

If the current data size exceeds the predetermined minimum data size (positive outcome or YES), the flow proceeds to nearest search function 1106 wherein a search of objects within the determined radius is performed. The flow then proceeds to return function 1108 and execution proceeds to perform other tasks.

FIG. 12 is a block diagram illustrating an exemplary computer system 1200 upon which an embodiment may be implemented. Computer system 1200 includes a bus 1202 or other communication mechanism for communicating information, and a processor 1204 coupled with bus 1202 for processing information. Computer system 1200 also includes a memory 1206, such as a random access memory (RAM) or other dynamic storage device, coupled to the bus 1202 for storing instructions to be executed by processor 1204. Memory 1206 also may be used for storing temporary variables or other intermediate information during execution of instructions to be executed by processor 1204.

Computer system 1200 is coupled via bus 1202 to display 1208, such as a liquid crystal display (LCD) or other display technology, for displaying information to the user. Input device 1210, described above, is coupled to bus 1202 for communicating information and command selections to the processor 1204.

According to one embodiment, computer system 1200 operates in response to processor 1204 executing sequences of instructions contained in memory 1206 or communication interface 1212. Such instructions may be read into memory 1206 from a computer-readable medium or communication interface 1212.

Execution of the sequences of instructions contained in memory 1206 causes the processor 1204 to perform the process steps described above. In alternative embodiments, hard-wired circuitry may be used in place of or in combination with computer software instructions to implement the embodiments. Thus, embodiments are not limited to any specific combination of hardware circuitry and software.

Computer system 1200 also includes a communication interface 1212 coupled to the bus 1202. Communication interface 1212 provides two-way data communication. For example, communication interface 1212 may be a wireless communication link. In any such implementation, communication interface 1212 sends and receives electrical, electromagnetic or optical signals which carry digital data streams representing various types of information.

Network link 1214 typically provides data communication through one or more networks to other devices. For example, network link 1214 may provide a connection through communication network 1216 to computer system 1200 or to data equipment operated by a service provider. The signals through the various networks and the signals on network link 1214 and through communication interface 1212, which carry the digital data to and from computer system 1200, are exemplary forms of carrier waves transporting the information.

Computer system 1200 can send messages and receive data, including program code, through the network(s), network link 1214 and communication interface 1212. Received code may be executed by processor 1204 as it is received, and/or stored in memory 1206 for later execution. In this manner, computer system 1200 may obtain application code in the form of a carrier wave.

It will be readily seen by one of ordinary skill in the art that the disclosed embodiments fulfill one or more of the advantages set forth above. After reading the foregoing specification, one of ordinary skill will be able to affect various changes, substitutions of equivalents and various other embodiments as broadly disclosed herein. It is therefore intended that the protection granted hereon be limited only by the definition contained in the appended claims and equivalents thereof. 

1. A method of determining density of a region of a map, comprising: determining one or more nodes of a quad tree applied to a map with which a predetermined query region intersects; calculating a cumulative data size of the query region based on a data size of the one or more intersecting nodes; and determining an average density of the query region based on the query region area and the cumulative data size.
 2. The method as claimed in claim 1, further comprising storing the determined query region density to a memory.
 3. The method as claimed in claim 1, further comprising outputting the determined query region density to an output device.
 4. The method as claimed in claim 1, wherein calculating comprises: adjusting the query region data size by an amount corresponding to the data size of a node enclosed by the query region; and adjusting the query region data size by an amount corresponding to the data size of a node proportional to the intersection area of the query region and the node.
 5. The method as claimed in claim 1, further comprising: specifying the predetermined query region based on at least one of user input, and a predetermined map display.
 6. The method as claimed in claim 1, wherein the determining comprises a query region in rectangular form.
 7. The method as claimed in claim 1, wherein the adjusting is performed for each of the one or more intersecting nodes.
 8. The method as claimed in claim 1, further comprising: automatically adjusting at least one of a detail level and a layer visibility of the map used to generate a map display having a feature density corresponding to a predetermined map feature density.
 9. The method as claimed in claim 8, wherein determining a density comprises determining a map density for at least one of one or more detail levels of the map and enabling visibility of one or more map layers.
 10. The method as claimed in claim 9, wherein automatically adjusting comprises at least selecting one predefined detail level of the map.
 11. The method as claimed in claim 9, wherein automatically adjusting comprises at least one of enabling visibility of one or more map layers and disabling visibility of one or more map layers.
 12. The method as claimed in claim 9, wherein automatically adjusting is performed for a determined map density greater than a predetermined maximum density threshold.
 13. The method as claimed in claim 9, wherein automatically adjusting is performed for a determined map density less than a predetermined minimum density threshold.
 14. The method as claimed in claim 9, further comprising: generating the map display based on the adjusted parameter.
 15. The method as claimed in claim 1, wherein determining density of selected map layers comprises determining street routing quality criteria.
 16. The method as claimed in claim 15, wherein the route quality criteria comprise at least one of urban route criteria and rural route criteria.
 17. The method as claimed in claim 15, wherein determining street routing quality criteria comprising urban route criteria is selected for a determined map density greater than a predetermined minimum urban density.
 18. The method as claimed in claim 15, wherein determining street routing quality criteria comprising rural route criteria is selected for a determined map density less than a predetermined minimum urban density.
 19. The method as claimed in claim 1, wherein determining map data size inside a query rectangle comprises enlarging a search radius by a predetermined amount for a determined map data size greater than a predetermined minimum data size.
 20. The method as claimed in claim 19, further comprises searching for objects to be displayed within the enlarged map radius.
 21. A mobile computer device for determining density of a map, the device comprising: a processor; a memory communicatively coupled with the processor and comprising a set of instructions which, when executed by the processor, cause the processor to: determine one or more nodes of a quad tree applied to a map with which a predetermined query region intersects; calculate a cumulative data size of the query region based on a data size of the one or more intersecting nodes; and determine a density of the query region based on the query region area and the cumulative data size.
 22. The mobile computer device as claimed in claim 21, further comprising instructions which, when executed by the processor, cause the processor to store the determined query region density to the memory.
 23. The mobile computer device as claimed in claim 21, wherein the instructions which cause the processor to calculate a cumulative data size further comprise instructions which, when executed by the processor, cause the processor to adjust the data size in the query region by an amount corresponding to the data size of a node enclosed by the query region and adjust the query region data size by an amount corresponding to the data size of a node proportional to the intersection area of the query region and the node. 24-27. (canceled)
 28. A computer-readable medium storing instructions which, when executed by a processor, cause the processor to determine one or more nodes of a quad tree applied to a map with which a predetermined query region intersects; calculate a cumulative data size of the query region based on a data size of the one or more intersecting nodes; and determine an average density in the query region based on the query region area and the cumulative data size.
 29. The computer-readable medium as claimed in claim 28, wherein the instructions which cause the processor to calculate a cumulative data size further comprise instructions which, when executed by the processor, cause the processor to adjust the query region data size by an amount corresponding to the data size of a node enclosed by the query region and adjust the query region data size by an amount corresponding to the data size of a node proportional to the intersection area of the query region and the node. 30-33. (canceled) 